Pith Number

pith:6L2WUPB4

pith:2013:6L2WUPB4BR7Y5NXA2Y2CJJ6OOV

not attested not anchored not stored refs pending

Spectral properties of Schr\"odinger operators on compact manifolds: rigidity, flows, interpolation and spectral estimates

Ari Laptev, Jean Dolbeault (CEREMADE), Maria J. Esteban (CEREMADE), Michael Loss

arxiv:1303.2790 v2 · 2013-03-12 · math.AP · math-ph · math.DG · math.MP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6L2WUPB4BR7Y5NXA2Y2CJJ6OOV}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T03:17:44.446758Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f2f56a3c3c0c7f8eb6e0d63424a7ce756d10cd0d4611a0a9a82ea652c1d1d316

Aliases

arxiv: 1303.2790 · arxiv_version: 1303.2790v2 · doi: 10.48550/arxiv.1303.2790 · pith_short_12: 6L2WUPB4BR7Y · pith_short_16: 6L2WUPB4BR7Y5NXA · pith_short_8: 6L2WUPB4

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/6L2WUPB4BR7Y5NXA2Y2CJJ6OOV \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: f2f56a3c3c0c7f8eb6e0d63424a7ce756d10cd0d4611a0a9a82ea652c1d1d316

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0101d10a34e64bc61497ae3dbc6522a109ca297b0a88d2f6569dec42219a3af1",
    "cross_cats_sorted": [
      "math-ph",
      "math.DG",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2013-03-12T07:02:24Z",
    "title_canon_sha256": "bb4a605de1cbc938e1759decfa338ff5d91f05763d5499e0768ac11877aacb9d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1303.2790",
    "kind": "arxiv",
    "version": 2
  }
}